"Drawing" single vertices obstructed by coordinate axes
You can press Ctrl + Space to toggle the 3d manipulator between visible and hidden. Or you toggle  it by clicking on it.





If you are referring to the fact that once you extrude you no longer see the manipulator that is because after you extrude you automatically go into grab mode, which will hide the manipulator. So if you want to move it along an axis you have two ways of doing this.

Method 1 (preferred)


Press E to extrude like you normally would
Constrain the extrude to an axis by pressing either: X Y Z


Method 2


Press E to extrude like you normally would
Drop the tool, RMB or Esc
Use the 3d manipulator to move it like you are used to